By the way, it is model number 917.270711.

That should be a Briggs 311707-0132-E1, which is OHV.
IF the problem seems to be getting past the compression stroke, the valves probably need adjusting.
Too much lash, and the compression release doesn't work.
Intake .004"
Exhaust .006"
+/- .001"
Piston 1/4" past TDC.

Thanks for the reply.

Just curious...Any reason why it will start with the charger connected, but not when it is disconnected (even though the battery has a good charge)?

Does one affect the compression stroke differently?

Thanks

Since it starts with the charger attached....

1) It may be that there is corrosion on the connection from the battery to the cables attaching to the battery. Are the metal to metal contacts clean? Especially the connector surfaces of the cables that mate with the battery? The charger would by-pass this connection.

2) Is it a "starter/charger" that provides a lot more power than just your battery?? If so, Bill K may be correct.

Well I will have to check when I get home, I'm not sure if it is a starter/charger. I know it has a 10 amp at 12V or 5amp and 24V (or something like that).

BUT - I did jump it off of a car originally, and it worked fine. Does that mean anything?

Your car will provide a LOT of cranking power. If it's just a 10 amp or so charger, it is near the same power as the tractor battery. You may want to try this, while attempting to start the tractor, wiggle the cables attached to the battery and see if it kicks over. This can be difficult to do depending on how your mowers safety systems are set up and the location of the battery. I have also rotated the engine manually by "rotating or turning" the fan cover attached to the flywheel at the top of the engine. This portion of the fly wheel is accessable on my mowers. If you can't turn it by hand, try rocking it. If it moves then, try starting again and refer to Bill K's post.

It is apparent that your battery is not supplying enough power to start your tractor, why that is - is the question. I agree that first you should really clean the inside of the battery cable terminals that attach to the battery. That won't cost you anthing.

I remember on cars if the engine got out of time it can make it very hard to start. I don't know if that is possible on a small engine.

Your battery is probably about 200 CCA (The owners manual specifies 190 CCA minimum). 10 more Amps from the battery charger is only about 5% more "capacity". Possibly enough to make the difference, but somewhat doubtful?

Others have mentioned cleaning the battery cables where they attach to the battery.
That's only PART of the job! The other ends of the cables are just as important, since they carry the same amount of current! Clean the connections where the ground cable attaches to the frame, battery + where it attaches to the starter solenoid and the cable connections between the solenoid and starter motor. Other potential, but not obvious , places are the starter motor case to engine block and engine block to the frame.
One other potential place of high resistance is the internals of the starter solenoid itself.

I'd still suspect the valve adjustment though. Cleaning connections is free, except for your time, however.

Check your battery connections and ground connections too.

pull the plug(s) and see if the motor will spin over - if it does your possibly looking at a valve adjustment (easy to do on an OHV motor - and Free)... i have witnessed huge improvements in starting - so don't discount this suggestion (if it applies in your case).

Or your solenoid is sick ...(about $15-$20) also easy to test/bypass with a set of jumper cables. you may want your choke on and ignition in the run position if you want to start your motor and exercise /test your running charging system as well...

or your Starter motor could be acting up ($75-$150)

Sorry I did not follow up sooner - things have been a little hectic around here with a newborn.

Well it looks like it was easy as just the cleaning connections. Now for the brake repair......